Announcements

• Midterm is here. It is due Tuesday, April 5 by 2:00 PM.
• Join the class form for cs270 on Piazzza.
• Homework 1 out Due. Feb. 12, 2011.
• Homework 2 out Due. Feb. 28, 2011.

Notes.

• Introduction and Routing/Toll Games. Draft Notes.
• Games Examples. Draft Notes.
• Maximum Weight Matchings. Draft Notes.
• Expert's algorithm. Draft Notes.
• Expert's algorithms Application to Min-Max for Games and Boosting. Draft Notes. We lifted material from Arora, Hazan, Kale: "Experts: The Multiplicative Weights Update Method: a Meta Algorithm and"
• Expert's algorithm for congestion minimization. Draft Notes.
• Linear Programming and taking a dual. Draft Notes.
• Perceptron, Support Vector Machine, the Kernel Trick. Draft Notes. Mostly from Avrim Blum notes.
• Sparse-cuts and the Spectrum. Draft Notes.
• Cheeger. Draft Notes.
• Random walks, volume estimation, sampling partial orders. Draft Notes.
• Cheeger Hard Part Draft Notes.
• Streaming Draft Notes.
• Streaming: Frequency Estimation Draft Notes.
• Cuckoo Hashing Draft Notes.
• Measure Concentration Draft Notes.
• Principal Components Draft Notes.
• Tree Metrics Draft Notes.
• Linear Systems Draft Notes.
• Linear Time Laplacian Draft Notes.
• Semidefinite Programming. Draft Notes.
• Fast Max flow Draft Notes.

Course Outline

This course will focus on some of the most important modern algorithmic problems, such as clustering, and a set of beautiful techniques that have been invented to tackle them. The techniques include the use of geometry, convexity and duality, the formulation of computational tasks in terms of two person games and algorithms as two dueling subroutines. We will also explore the use of randomness in MCMC type algorithms and the use of concentration bounds in creating small core sets or sketches of input data, which can be used to quickly get a reasonable solution. We will also explore the use of these new techniques to speed up classical combinatorial optimization problems such as max-flow.

* Routing Disjoint Paths - Toll/congestion game
* Two person zero-sum games, minimax theorem, minimum cost matching
* Experts/multiplicative weights algorithm
* Boosting
* LP duality, LP algorithms
* Support vector machines, VC Dimension
* Markov Chains, eigenvalues, Cheeger inequality
* Random generation, approximate counting, volume computation
* Measure concentration, load balancing, Cuckoo hashing, Bloom filters
* Johnson Lindenstrauss, locality preserving hashing
* Principal components analysis, learning Gaussians
* Streaming algorithms
* Fast linear systems solvers, electrical flows
* Fast max-flow
* SDP and applications
* Power law distributions.

Reading

Course Staff

Scheduling

Assessment

Course Outline

This course will cover material at the tougher end of an undergraduate algorithms course (in review), a bit beyond, and some that is well beyond, perhaps cresting on research oriented topics.

Topics covered will likely include...

Previous Notes